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Mathematician James Stewart is seen here at his 18,000 square-foot Rosedale Integral House Friday, August 29, 2014.Tim Fraser/The Globe and Mail

'Good evening, ladies and gentlemen, and welcome to my wake." That was how James Stewart welcomed a large crowd to the last of many concert evenings at his splendid Toronto home, Integral House. Dressed in a red brocade jacket, the eminent math educator stood to introduce several of the performers, though he was much weakened by the cancer that – as he said in the invitations – had left him with just weeks to live.

That was on Nov. 16. Dr. Stewart died on Dec. 3, after a full life devoted to his passions for mathematics, music, architecture and the more informal arts of bringing people together. He was 73.

Dr. Stewart was the author of the world's best-selling calculus textbooks, a series he began in 1980 and revised and expanded until the last months of his life. He was also a gifted violinist, who played chamber music whenever possible, and performed in the Hamilton Philharmonic and the orchestra at McMaster University, where he taught for three decades.

The money he earned from his textbooks, increased by astute investments, gave him the means to buy a ravine lot in Toronto and commission architects Brigitte Shim and Howard Sutcliffe to design Integral House, a curvaceous five-storey structure that ultimately cost $32-million. The house became renowned internationally, both for its organic form and for the excellent acoustics of its open concert room.

James Drewry Stewart was born in Toronto on March 29, 1941, to parents who had moved separately to the city from Saskatchewan. He was a good student in all subjects in elementary school, and at the age of seven began playing on a family violin sent from Saskatchewan by one of his grandmothers.

He wrestled more than once with the problem of which of his primary interests – music or mathematics – should become his career.

"I finally decided it would be better to be a mathematician whose hobby is music than a musician whose hobby is mathematics," he said.

He studied math and sciences at the University of Toronto and Stanford University, and did post-doctoral work at the University of London's Chelsea College, while continuing his violin studies at the Guildhall School of Music. Early in this process, he decided something was wrong with the way math was being taught.

"I remember him saying in first-year university, 'The professors really know their math, but they have no clue how to teach,'" recalls his sister, Sally Smith. From his first experience as a teaching assistant in London, he knew that he loved teaching and wanted to excel at it.

He co-wrote some high-school texts in the 1970s, but it took a suggestion from a couple of his students at McMaster for him to try writing a university-level calculus text. He spent seven years on it, saying later that with his teaching, research and writing, he worked 13 hours a day for 364 days of the year. That first book, published by Brooks/Cole, sold modestly at first, but by the time the second edition appeared in 1992, it was the bestselling work in the field.

"It was very well planned and thought out, and extremely easy to teach from," says Walter Craig, director of the Fields Institute for Research in Mathematical Sciences, where Dr. Stewart was a fellow. "Jim cared enormously about his students, and took pains to explain everything in steps that were of equal size."

Dr. Stewart constantly solicited reviews of his work from those who used the books, and attended to suggestions for improvement. He also kept abreast of the seismic changes in calculus education that began in the late 1980s. Fears that students were not fully engaging with the dry texts commonly in use prompted calls for a more contextual approach. Dr. Stewart sympathized with the movement, and incorporated its ideas into subsequent editions, while maintaining the thoroughness of a traditional textbook.

"There's lots of extra stuff, little historical details that bring the subject to life," says Deirdre Haskell, a McMaster math professor. "He was an amazing teacher, and really thought about mathematical thinking, and about how to communicate with students and let them know why we appreciate our subject."

At the heart of that appreciation was Dr. Stewart's passion for the beauty of calculus – for "the way it all fits together," as he said. It was similar to his feeling for the beauty of a sonata by Beethoven or Schubert, or for the many glass art works displayed in his home.

He often gave talks on the links between math and music, and mused about writing a book on the subject. At all stages during his adult life, he held musical salons in his home, where many of the guests were math colleagues who also loved music.

"When you talked to Jim he was calm, organized and rational, but when he played the violin he was none of those things," says William Ralph, a long-time friend, pianist and mathematician who often played chamber music with Dr. Stewart. "He was so passionate. The second he touched that violin he became a different person."

He took an interest in promising younger musicians, often featuring them in his house concerts. His final salon at Integral House included a performance by 20-year-old violinist Blake Pouliot, for whom Dr. Stewart was trying to arrange the purchase of a Guarneri violin.

Integral House was initially intended to be a larger venue for his private concerts, but soon evolved into a project of life-changing significance. It became a coveted site for benefit concerts featuring the likes of Steve Reich and Philip Glass, and for special events designed to help groups and organizations Dr. Stewart cared about.

"So many of the events he had were really about friend-making, having people understand what these groups were capable of, and allowing them to do their work," Ms. Shim says. As for the decade-long process of planning and building Integral House, Ms. Shim said he approached it with the intensity that characterized all his pursuits.

"Jim appeared very low-key and understated, but he was also really ambitious," Ms. Shim says. "If he was going to write a textbook, it would be the best you can possibly do, and rock the world of calculus textbooks. And I think that's what he wanted to do architecturally."

The house and all its custom-designed furnishings were an expression of his love of curves, so prominent in calculus. But there was no "formula" for the house, he said – it was a work of art that he was lucky enough to live in, and that brought him into contact with musicians he might otherwise never have met.

It also became a great party centre during Pride Week and at Halloween, when the all-male guests were expected to show up in extravagant drag. "He was a crazy guy, privately," Mr. Ralph says. "That man could party. He would let it all go."

Dr. Stewart was "out" his whole adult life, and supported many services and initiatives for LGBT people. Joseph Clement, who is making a documentary about Integral House and its owner, said that in the early 1970s, Dr. Stewart helped launch the Pride movement in Hamilton by inviting Toronto activist George Hislop to speak in the city.

"It really galvanized the movement there," Mr. Clement says. "The following year, the first Pride march happened in Hamilton."

Mr. Clement's cameras had been following Dr. Stewart around for months when he was diagnosed with advanced multiple myeloma last spring. His response, Mr. Clement says, was typically low-key

"He was like, 'The news is not good. It looks like I'm dying. Do you still want to do the shoot on Monday?'" Mr. Clement recalls. "Jim could be very deadpan about things. But I think there was a lot of bravado, even in the way he died. It was about going out the way he wanted to go."

In July, a few months after suffering a broken hip related to his cancer, Dr. Stewart made a last trip to severa European cities with a few friends. In Prague, he wanted to visit Hradny Castle, which stands at the top of a slope that seemed a daunting obstacle for a man with mobility issues.

"He wanted to walk with us," says Riko Gunawan, a close friend who helped care for Dr. Stewart in his last months. "And I said, 'Jim, do you want me to get you a wheelchair or a cane?' And he said, 'No, if I can't do this, I'm not going to travel.' He was really brave, he walked all the way. It took him a long time, but he managed to do it without anybody's help."

Dr. Stewart was a rationalist who had no faith in an afterlife, and wanted no ceremony performed after his death. His name, however, will persist in the James Stewart Centre for Mathematics at McMaster, and his thoughts about calculus will continue to inspire students for years and possibly decades to come.

His final act was one of surpassing generosity. He instructed his executors to sell Integral House, and give the money to organizations he supported during his life.

Mr. Stewart leaves his sister, Ms. Smith; his brother, Alan; his niece, Jacqueline; nephew, Kelly; and their families.

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